Three blocks of masses m₁ = 5 kg , m₂ = 3 kg , and m₃ = 2 kg are placed in contact with each other on a frictionless horizontal surface. A constant horizontal force F₁ = 50 N is applied on m₁ to the right, and another constant horizontal force F₂ = 10 N is applied on m₃ to the left, as shown in the figure. What is the ratio of the normal contact force between m₁ and m₂ to the normal contact force between m₂ and m₃ ?

Step-by-step solution

Let the common acceleration of the system be a . The net force on the system is F_ net = F₁ - F₂ = 50 - 10 = 40 N . Total mass of the system is M = m₁ + m₂ + m₃ = 5 + 3 + 2 = 10 kg . The acceleration is a = F_ net M = 40 10 = 4 m/s ^2 . Let N₁ be the normal contact force between m₁ and m₂ . Considering the free body diagram of m₁ : F₁ - N₁ = m₁ a 50 - N₁ = 5 4 N₁ = 30 N Let N₂ be the normal contact force between m₂ and m₃ . Considering the free body diagram of m₃ : N₂ - F₂ = m₃ a N₂ - 10 = 2 4 N₂ = 18 N The ratio o